52 



S. L. Penfield — Crystal Dr diving. 



other hexagonal axes, therefore, must intersect great circles pass- 

 ing through — a z and X, and — a % and J", at 60° from — a % and a 3 . 

 To find the desired intersections on the great circle at right 

 angles to one of the twinned axes, c ; through the 60° gradua- 

 tion points on the horizontal ellipse to the left, figure 20, draw 

 the chords xx' parallel to a chord through — B aud X; like- 

 wise through the 60° points on the horizontal ellipse to 

 the right draw the chords yy' parallel to a chord through B 

 and X. The intersections of the chords xx' and yy' determine 

 the extremities of the horizontal axes a^ — «„ and <2 2 , — a v To 

 make the drawing somewhat more real, a hexagon at right 

 angles to the twin axis cc has been constructed, by uniting the 

 ends of the horizontal axes. Following a similar process 

 2i 22 (drawing chords parallel to B Y 



and - B Y through the 60° grad- 

 uation points of the horizontal 

 ellipse) the extremities of the 

 horizontal axes at right angles 

 to the twinned axis C would be 

 found, but it has not seemed 

 best to complicate the figure 

 by carrying out this construc- 

 tion. The length of the vertical 

 axis of calcite is 0*854, and this 

 is plotted on the vertical axis 

 by laying off three times 0*854 

 (2*562) on the perpendicular, using the scale of decimal parts, 

 and proportioning the length on the twinned c axis by con- 

 structing the parallel lines pp and p'p', as indicated in figure 

 20. Figure 21 represents the scalenohedron v { 2131 } of calcite 

 drawn on the twinned axes, and figure 22 is a development like 

 that observed on the crystals from Union Springs, 1ST. Y., 

 where the re-entrant angle is obliterated by the extension of 

 four of the faces, resulting in a peculiar spear-head shaped 

 development. 



Use of T-square and, special Triangles. — A T-square may 

 be used to advantage in connection with the engraved axes, 

 figures 9 and 10, the paper PP, figure 23, being adjusted on 

 a drawing board BB so that the blade of the T-square is 

 parallel with the right-to-left or h axis of the clinographic pro- 

 jection. If an ordinary rectangular drawing board is used, the 

 paper may be fastened somewhat askew upon it, and it is not at 

 all necessary to have a board with its right-hand edge cut at a 

 special angle, as shown in figure 23. Special triangles have also 

 proved to be very convenient. One of these is a truncated 

 triangle 7, figure 23, so made that when its lower edge is 

 against the blade of the T-square its upper edge is parallel to 



